These results and more are mentioned in Proposition 1.1.5 of Coxeter Graphs and Towers of Algebras by Goodman, de la Harpe, and Jones, 1989.
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Jonas MeyerMay 9 '10 at 9:05

59

Wait, did you just tell Vaughan Jones about his own paper? MO has jumped the shark.
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Ben Webster♦May 9 '10 at 14:26

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Perhaps I should end up with a negative score because of this... However I assure you that one does not have to be gaga to have forgotten what was in a book one wrote with 2 coauthors over 20 years ago. Looking at it it seems that the Shearer result was not yet published when our book was finished-it does not seem to be mentioned in the appendix I which is the only place I looked in the book when looking for the answer to the question. Apologies, especially to Pierre if he reads this, Vaughan Jones
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Vaughan JonesMay 9 '10 at 15:52

5

The set of limit points was vaguely reminiscent of the set of possible Jones indices, which is why I looked. I found the proposition using the listing of $(2+5^{1/2})^{1/2}$ in the index. I then hesitated to mention it, not wanting the comment to be seen as criticism--but I had to. We haven't met, but I imagined it would be worth a laugh. No need to apologize.
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Jonas MeyerMay 9 '10 at 17:34

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@Everybody- No worries. It's a good thing that this tidbit is sitting somewhere on the internet, waiting to be found by google (try googling some combination of title key words, you'll see this page is quite high). I, at least, am of the opinion that anything that gets more good content on the site is a good thing. It's also good to see you here, Vaughan.
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Ben Webster♦May 9 '10 at 18:15